Description
Given a binary matrix, you may toggle any row or column. Return the maximum possible score, where each row is a binary number.
Examples
Input:
grid = [[0,0,1,1],[1,0,1,0],[1,1,0,0]]Output:
39Explanation:
Optimal flips maximize sum.
Input:
grid = [[1]]Output:
1Explanation:
Minimal case with a single-element matrix.
Input:
grid = [[1,0,1],[0,1,0],[1,0,1]]Output:
21Explanation:
Initial matrix represents binary numbers: row 0 = 101 (5), row 1 = 010 (2), row 2 = 101 (5), sum = 12. To maximize, the goal is leftmost bits to be 1. Toggle column 1 to get [[1,1,1],[0,0,0],[1,1,1]]. Now row 0 = 111 (7), row 1 = 000 (0), row 2 = 111 (7). Toggle row 1 to get [[1,1,1],[1,1,1],[1,1,1]]. Final sum: 7 + 7 + 7 = 21.
Constraints
- •
1 ≤ m, n ≤ 20